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On the application of the theory of uniform distribution to the solution of differential equations. (Über die Anwendung der Theorie der Gleichverteilung auf die Lösung von Differentialgleichungen.) (German) Zbl 0973.11075

Summary: We consider systems of ordinary differential equations and their set of initial conditions. The author showed in his papers about the so-called “willkürliche Funktionen von Poincaré” that it is only necessary to use a set of initial conditions having a tensity to construct numerical approximations for the whole set of the initial conditions. To make the calculation of the approximate solution simpler, e.g. for linear equations we use Bernstein polynomials. We construct further approximate tensities in the theory of uniform distributions in the general form. In the appendix we make further comments on this subject for general manifolds.

MSC:

11K36 Well-distributed sequences and other variations
34A45 Theoretical approximation of solutions to ordinary differential equations
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